A Fashionable Partial and Heterogeneous
mirror for Modality
Antonia Huertas and María Manzano
The aim of this paper is
twofold: In the first place we present a partial and heterogeneous mirror
for modality which serves to build a modal predicate partial logic; in
the second place, we propose a general method to redesign a logic.
In both cases the starting point
is a logic non totally developed or accepted, which we call here a prelogic.
From a complete analysis of this prelogic, we build a possibly partial
and heterogeneous logic which serves as the underlying logic of the whole
construction to be carried out afterwards.
Once we have our partial and heterogeneous
logic, PHL, we should define a translation of formulas of the original
logic into PHL and a conversion of structures of the original logic into
the partial and heterogeneous structures.
As a result of this process, we
obtain a theory in PHL representing the original logic.
In correspondence theory, where
the logics we study are well equipped, with a proper semantics, this is
the end of the story. But in our case we use the mirror image to build
an improved logic in the real world.